Damped multichannel singular spectrum analysis for 3D random noise attenuation

Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation in seismic data, which decomposes the vector space of the Hankel matrix of the noisy signal into a signal subspace and a noise subspace by truncated singular value decomposition (TSVD). However, this signal subspace actually still contains residual noise. We have derived a new formula of low-rank reduction, which is more powerful in distinguishing between signal and noise compared with the traditional TSVD. By introducing a damping factor into traditional MSSA to dampen the singular values, we have developed a new algorithm for random noise attenuation. We have named our modified MSSA as damped MSSA. The denoising performance is controlled by the damping factor, and our approach reverts to the traditional MSSA approach when the damping factor is sufficiently large. Application of the damped MSSA algorithm on synthetic and field seismic data demonstrates superior performance compared with the conventional MSSA algorithm.